Szeg\H{o} Recurrence for Multiple Orthogonal Polynomials on the Unit Circle
Classical Analysis and ODEs
2024-05-02 v1 Spectral Theory
Abstract
We investigate polynomials that satisfy simultaneous orthogonality conditions with respect to several measures on the unit circle. We generalize the direct and inverse Szeg\H{o} recurrence relations, identify the analogues of the Verblunsky coefficients, and prove the ChristoffelDarboux formula. These results stand directly in analogue with the nearest neighbour recurrence relations from the real line counterpart.
Cite
@article{arxiv.2404.18666,
title = {Szeg\H{o} Recurrence for Multiple Orthogonal Polynomials on the Unit Circle},
author = {Marcus Vaktnäs and Rostyslav Kozhan},
journal= {arXiv preprint arXiv:2404.18666},
year = {2024}
}